From Peaks to a Wave
Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 32 of 51.
A top and the bottom right after it fix a whole wave. Say the highest point is (π/2, 5) and the next lowest is (3π/2, 1).
k = (5 + 1)/2 = 3
The amplitude is (5 − 1)/2 = 2. From a top to the next bottom is half a period, so the period is 2 × π = 2π. A sine reaches its top a quarter period after it crosses its midline going up, and a quarter of 2π before π/2 is 0: the wave is a sine starting at 0.
On the board, place the dot on the midline and the dot on the top. The rest of the wave follows.
Challenge
A sine wave has its highest point at (π/4, 3) and the next lowest point at (3π/4, −1). Draw it. Press Check.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Graphs of Trig Functions
1From Circle to Wave
Ride a Ferris WheelHeight on the Unit CircleUnrolling the Sine GraphThe Sine Graph in RadiansCircle to Wave Recap7Reading a Graph
The Equation of a WaveSine or Cosine?From Peaks to a WaveAll Four at OnceReading Recap